1. Field of the Invention
The present invention relates to an estimation device that estimates a hidden state from observed data.
2. Description of Related Art
Conventionally, an image that is taken by a camera has been used as observed data in order to detect a state of an estimated object (e.g., a head posture (the state) of a driver (the estimated object) while driving) without restraining the estimated object.
However, in such a case, only brightness and color information of each picture element are directly obtained from the image as the observed data, and thus the head posture cannot be directly detected from the image.
The state (e.g., the head posture) of the estimated object cannot be directly detected from the observed data (the image), and such the state of the estimated object is defined as a hidden state. Time-series Bayesian estimation is known as a method for calculating posterior probability distribution of the hidden state of the estimated object based on the observed data.
Generally, the time-series Bayesian estimation cannot be analytically solved, since complex integration calculation is involved in deriving distribution of various model variables (including a hidden state variable). Nevertheless, a Kalman filter allows integration calculation, which is involved in calculation of the posterior probability distribution of the hidden state of the estimated object, to be analytically carried out, provided that probability distribution of a model variable conforms to Gaussian distribution, and that a system equation that defines a model has linearity. Using the Kalman filter, a method for rapidly performing the time-series Bayesian estimation is known. (For example, see A. Blake et al. A frame work for spatio-temporal control in the tracking of visual contours. International Journal of Computer Vision, 11, 2, pp. 127-145, 1993.)
However, when it comes to estimation of the driver's head posture, a complex disturbance (non-Gaussian noise) is applied to the observed data in an actual environment. This complex disturbance is caused by a complex movement of a head region, a rapid change in a lighting condition (due to, for example, direct sunlight, west sun, and a street lighting), and existence of shieldings such as the driver's hand and cap. Therefore, because the probability distribution of the model variable does not conform to the Gaussian distribution, or the system equation deviates from the linearity, it is generally difficult to obtain stable estimation accuracy by means of the Kalman filter.
Besides, when the image is used as the observed data, a dimension of the model variable generally often becomes high. Consequently, a very massive amount of throughput is generated due to the above integration calculation, and performing the time-series Bayesian estimation using the Kalman filter in real time is very difficult.
By comparison, a particle filter, which conducts time series estimating and predicting of the hidden state by means of approximative time-series Bayesian estimation, based on the observed data to which the non-Gaussian noise is applied, is known.
The particle filter discretely expresses prior probability distribution and the posterior probability distribution of the hidden state for each instant of time using a finite number of particles, thereby performing the time series estimating and predicting.
The number of particles needs to be large, in order to achieve high approximate accuracy of the posterior probability distribution through the particle filter. On the other hand, the number of particles needs to be curbed for the sake of real-time processing. That is, there is a trade-off relationship between accuracy and processing time when the particle filter is employed.
As a result, a method called Rao-blackwellization, which makes compatible an improvement in estimation accuracy and a curb on a computational complexity using a relatively small number of particles, is known. (For example, see G. Casella and C. Robert. Rao-blackwellization of sampling schemes. Biometrika, 83, 1, pp. 81-94, 1996.) Through the Rao-blackwellization, state variables are divided with analytical integrability, and the particle filter is used only for the state variables that are not analytically integrable, thereby rendering small the dimension involved in estimation using the particle filter.
The Rao-blackwellization is applied to the field of image processing as well, and a method for making compatible the improvement in the estimation accuracy and a curb on the processing time by rendering small the dimension involved in the estimation at the particle filter is known. (For example, see A. Doucet et al. On sequential Monte Carlo sampling methods for Bayesian filtering. Statistics and Computiong, 10, 3, pp. 197-208, 2000.) A probability system (a higher layer) that includes the hidden state of the estimated object and an intermediate hidden state is divided from the probability system (a lower layer) that includes the intermediate hidden state and an observable state. The higher layer allows a linear Gaussian process to be presupposed, whereas the lower layer does not. Generally, this division is made by creating the intermediate hidden state (e.g., coordinates of a plurality of facial feature points in an image plane), which has a causal relationship both with the hidden state of the estimated object and with the observed data, between the hidden state of the estimated object and the observed data. The Kalman filter, for example, is employed for the time series estimating at the higher layer, and the particle filter is employed for the time series estimating at the lower layer. Accordingly, the dimension involved in the estimation at the particle filter is rendered small, so that the improvement in the estimation accuracy and the curb on the processing time can be made compatible.
Additionally, while an application of the Rao-blackwellization requires a part of the state variables being analytically integrable, this is not limited to the Kalman filter that corresponds to a linear Gaussian process model (e.g., a mixed normal distribution model, a hidden Markov model, and a Dirichlet process model).
However, in the above method described in A. Doucet et al. (2000), a result (the posterior probability distribution of the intermediate hidden state) of estimation of the intermediate hidden state through the particle filter at the lower layer is used as the observed data, which is to be employed for estimation of the hidden state of the estimated object at the higher layer. Consequently, a lowering of the estimation accuracy of the intermediate hidden state at the lower layer leads to the lowering of that of the hidden state of the estimated object at the higher layer. Furthermore, once the estimation accuracy of the intermediate hidden state lowers at the lower layer, it has generally been difficult to restore this estimation accuracy to its normal state.
For instance, the particle filter used for estimation at the lower layer may be configured for the time series estimating of the coordinate (the intermediate hidden state) on the image (the observed data), onto which a certain feature point of the driver's face is projected. In such a case, when a similar point (that is referred to as a false feature point) to the feature point exists in the observed data, this false feature point, as well as the feature point, has great likelihood. For this reason, in a case where the feature point moves irregularly and rapidly, for example, a particle group that discretely approximates the priori and posterior probability distributions of the intermediate hidden state may deviate from the feature point and may be captured by the false feature point. Once the particle group is captured by the false feature point, the particle filter, from that time onward, carries out the following observation and estimation using the particle group that conforms to a prediction (the prior probability distribution of the intermediate hidden state), which has been produced from a result (the posterior probability distribution of the intermediate hidden state) of the estimation of the coordinate of this incorrect feature point. Therefore, it becomes difficult to bring the particle group out of an abnormal state in which they track the false feature point.